A Distance-Speed Word Problem?

Question

Joe is driving from his home in Alpha to a city down the Interstate 200 miles away where the Alpha Lions have a football game. The route is not a straight line, however. He will drive west for 120 miles, then south for 60 miles, then east for the last 20 miles.

However, Joe's roommate Pete does not believe the Interstate is the way to go, since the distance from Alpha to the game is fewer miles by regular highway and city streets than by the Interstate. Pete knows he cannot drive quite as fast, but believes he can get to the game quicker going his direct route.

Joe thinks Pete is overly optimistic, reminding him of the stop lights, school zones and traffic along the way that will slow him down.

If Joe averages 60 mph on the Interstate, what will be Pete's average speed have to be to make good on his goal of being at least as quick to the game as Joe?

Assume that Pete's route is a straight line from Alpha to the game. Tell me how you did the calculation.

Answer 1

Draw the diagram.

Let AB (negative x-axis) =  120

BC(parallel to negative y-axis in third quadrant) = 60

CD(parallel to x-axis towards + x-axis) = 20

join AD. Draw DE perpendicular from D to AB.

now AED is a right angled triangle.

AD = hypotenuse

AE = 100

ED = 60

AD^2 = 100^2 + 60^2 = 13600

AD = 20 sqrt(34)

so the distance travelled by Joe = 20sqrt(34)

time taken by Joe to reach game = distance/speed

=> 20sqrt(34)/60= sqrt(34)/3  = 1.944 h

so Pete's average speed should be = distance / time = 200/1.944

=> 102.9 mph

Answer 2

Draw a horizontal line right to left (west), label it 120. Draw a line down (south), label it 60. Draw a line left to right (east), label it 20. Try to draw the lines roughly to scale. Draw a line from the beginning point to the ending point (it should angle down and to the left, label it H). Draw a line straight up from there, at a 90 degree angle to the first line you drew above (west - 120 miles). You should now have a right triangle that is 100 x 60 x H. Solve the triangle for the hypotenuse (H) > This is Pete's distance. Now you can figure out the speed Pete needs to travel.

Answer 3

200 miles by interstate, 116 direct, time is 200/60 so the speed be needs to beat is 112/200/60 so that's 33.6mph.

I left out what the other guy says.

You don't learn much by getting your school work done by us, but I'm willing to help you kill your future.